1. Field of the Invention
The present invention concerns computer-implemented and/or computer-enabled methods, systems, and mediums for enabling improved feedback and feedforward control during process control. More specifically, one or more embodiments of the present invention relate to run-to-run control, including determining offset and feedback threshold values during real-time process control, particularly in connection with semiconductor manufacturing.
2. Description of the Related Art
Detecting and controlling errors during a manufacturing process is an important goal. This is particularly true in connection with the process of manufacturing semiconductors. During the manufacturing process, various measurements are made in order to detect and/or determine errors e.g., to detect when an observed value differs significantly from an intended target result. When the difference is sufficient, the manufacturing process control system will attempt to control (e.g., compensate for) the error so as to continue to produce products (e.g., chips) that are within acceptable ranges or tolerances from the target result. The difference between the target and measured values that will trigger a compensation operation is known as the threshold error or feedback threshold.
It has been observed that material such as a wafer that is processed in connection with a semiconductor manufacturing process will inevitably include at least some error or some deviation from the intended target result or specification. In order to determine when it is desired to perform additional control in order to make an adjustment during processing, conventional systems utilize a feedback threshold as a trigger. Whenever a compensation or control operation is triggered and the adjustment is made, however, the result following the adjustment still will usually deviate from the intended target result. Further, there are tolerances within which a tighter adjustment of a control does not effectively cause the material to be processed closer to specification, since the control is simply not capable of a sufficiently fine adjustment.
Conventionally, control of an error is attempted when one or more preconditions assigned to the tolerance range for the target specification using a statistical approach are satisfied. The conventional statistical approach employs a standard deviation. Nevertheless, even when the process control system uses standard deviation as the threshold value, there is always a lack of precision, or a tolerance range within which it is not truly possible to control more tightly.
Typically, a statistical process variance or standard deviation that is determined under optimal conditions as an estimation of processing error. Specifically, current methods predetermine the amount of an observed output that is unadjustable process noise, and thus the range that the controller cannot further improve upon, in an open-loop (i.e., no feedback). This predetermined amount is then applied to (e.g., subtracted from) the actual measurements derived from the device, process and/or material being measured. Thus, statistical process variance measured while the process, material to be processed, and processing device conditions are at an atypically pristine state is used as a substitute for what would otherwise be a truer (e.g., more real world) measurement of a process variance. The measurement at this atypical condition is then used as an estimation of the processing variance occurring throughout the manufacturing process under consideration.
Statistical use of standard deviation in connection with observed deviation is illustrated, for example in “Statistical feedback control of a plasma etch process”, P. Mozumder et al., IEEE Transactions on Semiconductor Manufacturing, Vol. 7, No. 1 (February 1994). The statistical variance Sk at the kth run is calculated using the standard deviation as:
                              s          k                =                                            1                              n                -                1                                      ⁡                          [                                                                    ∑                                          i                      =                      1                                        n                                    ⁢                                      X                                          k                      -                      i                      +                      1                                        2                                                  -                                                      n                    ⁡                                          (                                              X                        _                                            )                                                        2                                            ]                                                          (        1        )            
where,
n=number of samples
x=deviation of observed value from predicted value
The conventional process control system compares the observed standard deviation to a threshold in order to determine if the deviation is acceptable. Once the standard deviation greater than the threshold is detected, the process model's tuning procedures for increasing control are invoked. In the conventional process control method, the standard deviation is used to determine the level for the threshold or trigger. Within the threshold, it is assumed that the deviation cannot be sufficiently controlled.
The conventional use of measurements at pristine conditions in estimating threshold error, despite its industry acceptance, is not a reasonably accurate reflection of process error during real manufacturing conditions. One of many reasons that measurements at pristine conditions do not reasonably reflect true conditions is that materials such as wafers processed in most front and back end processing devices in the semiconductor industry have relationships or effects on subsequently processed wafers between runs (“run-to-run”). Accordingly, conditions applied to and/or affected by wafers that were previously processed in a processing device will have residual effects on wafers that are currently being processed in that processing device. An estimation of threshold error derived from measurements taken while the processing device is at a steady state, consequently, does not reflect the fluctuations introduced during run-to-run processing.
Therefore, there remains a need to have improved control, particularly within a tolerance range associated with a target specification. There also remains a need to address the effects of run-to-run conditions on such measurements.